In theory. In practice, the code will often have corner case behaviours that eludes any of the tests, yet are still important.

As an aside, as I understand it, refactoring was popularised as a response basically to this conundrum - it's a technique for reorganising code without changing its functionality. So you can gradually "rewrite" your two page function without losing the accumulated knowledge.

Unless we really stretch the word "refactor", my "in practice" is different than yours. I've done plenty of re-writes that fixed more unknown bugs than re-opened previously solved ones.